Moments after the fiscal cliff was averted, President Barack Obama strode to the White House podium to thank congressional leaders from both parties and remind them of other policy challenges ripe for bipartisan co-operation.

What followed was an ambitious list of second-term priorities: immigration reform, climate change, lifting domestic energy production and gun control, on top of perhaps the most important issue, finding ways to lift the economy and incomes.

"It's not just possible to do these things, it's an obligation to ourselves and to future generations, and I look forward to working with every single member of Congress to meet this obligation in the new year," he said.

The measured peace offering from Mr Obama to Republicans in Congress, however, will run up against a much more rancorous reality on Capitol Hill and promises to make any second-term gains painfully difficult.

The confrontation over the fiscal cliff legislation, which Mr Obama signed into law late on Wednesday night, has further undermined relations between Mr Obama and his most important negotiating partner in Congress, John Boehner, the Republican House speaker.

"I don't think either of them regards the other as being able to deliver his own troops," said William Galston, a former Clinton administration official, now at the Brookings Institution.

Within Congress, relations between the Democratic and Republican Senate leaders, Harry Reid and Mitch McConnell, two old warhorses who can usually find ways to do business, also foundered in the fiscal cliff talks.

The forthcoming confrontations will probably have a similar impact, as Republicans feel they enter talks over raising the debt ceiling in the coming weeks playing a far stronger hand than they had in the fiscal cliff.

Under the fiscal cliff, taxes were going up no matter what Republicans did. The debt ceiling, however, cannot be lifted unless they vote for it.

Dave Camp, who chairs the congressional committee overseeing tax policy, said that House Republicans had not settled on a strategy for the debt ceiling but the central aim was to leverage it to cut spending further.

"Before we raise the debt limit we have to reduce spending," Mr Camp said.

Many Republicans are less diplomatic in private and see the debt ceiling fight as a chance to get revenge both on the White House and the dealmakers within their own party for being forced into accepting a tax increase this week.

Of all the issues crowding Mr Obama's agenda, immigration has the best hope of passing in some form, as the disastrous vote recorded by Republicans among minorities in 2012 gives them a huge incentive to address the issue.

But on everything else, with the Republicans remaining in control of the House, Mr Obama needs all the skills of cajoling, seducing and manipulating Congress that he has so far shown no signs of developing.

"I find it remarkable that the president apparently continues to believe that he will not have to deal with people that he does not agree with," said Mr Galston. "A president who is not disdainful of the art of legislating can get things done."

Forging a consensus on issues such as gun control and climate change, if the White House does take them on, will require Mr Obama to do more than just persuade some Republicans to support him.

Many Democrats are wary of such reforms or oppose them outright, and a second-term president with declining political capital will face an uphill battle to shift their views.